I think fisicx nails this SesO. There are many tried and tested ways to get people signing up for your newsletter from landing pages with cheap FB ads, to popups, to giveaways, to downloads... but why have a newsletter?
I went down this route for years with no plan. I got thousands of subscribers to my weekly newsletter with a great open rate. However, it was just a drain on my time, a big monthly cost for email marketing and a bit of an ego trip until I figured out how to use it to grow my business.
Are you clear on how you'll monetise your newsletter? Will you be using it to recruit clients, sell services, products, etc.? If not, it may just be better to put your energy elsewhere until you have a plan.
And if you've got a plan - great!
If you have traffic to your site already then downloads, ebooks, mini-courses, white papers, etc from pop-ups are what I've found to be most effective. If you don't have organic traffic, then you will need to pay for a flow of it to a landing page - which is why you need to know how you'll monetise your email.